Project 3: Multiple Response Optimization in Beer Brewing

Maj Beau Nunnally, Capt Kevin Farley, 2Lt Stuart Corbett

November 28, 2016

Background

Background

  • Barley, the most widely adapted cereal grain in the world, is an ancient crop that has been used for thousands of years for feed, food, and the production of beer.

  • The process by which barley is converted into a usable form for brewing is called malting.

Dependent Variables (Responses)

Response Units
Amylase Level (Goal:Max) (U/G)
Superoxide Dismutase (SOD) Level (Goal:Max) (U/G)
Dymethyl Sulphide (DMS) (Target: 65 ppb ) Parts per Billion (ppb)

Independent Variables (Factors)

Factor Minimum Maximum
Seeping Temperature 14°C 18°C
Seeping Time 24 hours 48 hours
Germination Temperature 12°C 20°C
Hydrogen Peroxide 0 g/L 0.2 g/L
Germination Time 4 hours 8 hours
Withering Temperature 35°C 50°C
Drying Temperature 55°C 65°C
Kilning Temperature 70°C 90°C
IDK Level 1 Tufnel 11 Tufnels

Methodology

Stage 1: Variable Selection

  • We conducted a variable screening experiment over entire feasible region.
  • Using a Definitive Screening Design (with JMPs automatic formulation)
    • Because it does not alias main effects
    • Uses small number of design points
    • Correlation structure should have minimal impact on determinations
  • Performed Stepwise selection for model parameters for each Response
  • Purpose:
    • Identify main effects to include in model building

Stage 2: Model Building

  • We fit model using a CCD, face-centered and four center-points.
    • Assumes variable reduction successful
    • High power relative to runs
    • Good picture of surface

Stage 3: Data Analysis

  • Using model runs from Stage 2, desirability functions are used to determine optimal points
    • Include both Additive and Multiplicative functions
    • Develop recommendation for Decision Maker

Analysis: Stage 1

Variable Selection for Amylase Level

Anova Table for reduced model for Amylase Level
  Estimate Std. Error t value Pr(>|t|)
Steeping_Time 50.82 26.25 1.936 0.06973
Germination_Temp 80.67 26.25 3.073 0.006893
Kilning_Temp 165.9 26.25 6.32 7.679e-06
(Intercept) 733.8 24.31 30.19 3.287e-16

Variable Selection for SOD Level

Anova Table for reduced model for Superoxide Dismutase Level
  Estimate Std. Error t value Pr(>|t|)
Steeping_Time 44.6 13.35 3.34 0.003883
Germination_Temp 153.6 13.35 11.5 1.92e-09
Kilning_Temp -165.6 13.35 -12.4 6.066e-10
(Intercept) 937.4 12.36 75.81 5.934e-23

Variable Selection for DMS

Anova Table for reduced model for Dymethyl Sulphide
  Estimate Std. Error t value Pr(>|t|)
Steeping_Time 7.4 1.4 5.4 4.9e-05
Germination_Temp 21 1.4 15 3.1e-11
IDK_Level 2.1 1.4 1.5 0.15
(Intercept) 38 1.3 30 4.5e-16
Anova Table for reduced model for absolute value of Dymethyl Sulphide
  Estimate Std. Error t value Pr(>|t|)
Steeping_Time -4.982 1.118 -4.458 0.0003042
Germination_Temp -18.17 1.118 -16.26 3.334e-12
(Intercept) 29.44 1.035 28.46 2.036e-16

Analysis: Stage 2

Model for Amalyse

Anova Table For Amylase Level
  Estimate Std. Error t value Pr(>|t|)
Steep_Time 38 21 1.8 0.097
Germ_Temp -121 21 -5.8 9.1e-05
Kiln_Temp 138 21 6.6 2.7e-05
I(Germ_Temp^2) -90 32 -2.8 0.015
Steep_Time:Germ_Temp 45 24 1.9 0.078
(Intercept) 975 24 41 2.5e-14

Model for SOD Level

Anova Table For SOD Level
  Estimate Std. Error t value Pr(>|t|)
Steep_Time -52 18 -2.9 0.013
Germ_Temp 114 18 6.5 4.6e-05
Kiln_Temp -146 18 -8.3 4.6e-06
I(Germ_Temp^2) 51 26 1.9 0.081
Steep_Time:Germ_Temp -61 20 -3.1 0.01
Steep_Time:Kiln_Temp -36 20 -1.8 0.095
(Intercept) 1029 20 52 1.6e-14

Model for DSD Distance

Anova Table For DSD Distance from 65
  Estimate Std. Error t value Pr(>|t|)
Steep_Time -1 1.3 -0.8 0.44
Germ_Temp -8.3 1.3 -6.5 1.4e-05
I(Steep_Time^2) 4.8 1.9 2.5 0.026
(Intercept) 10 1.4 7 6.7e-06

Resulting Surface Plots

Contour Plots for Amylase
Contour Plots for Amylase

Resulting Surface Plots

Contour Plots for SOD
Contour Plots for SOD

Resulting Surface Plots

Contour Plots for DSD
Contour Plots for DSD

Analysis: Stage 3

Pareto Front

  • 9261 observations (0.1 incriments on each variable)

  • The Pareto Front reduced this to 1621 observations

3D Scatter Plot of Pareto Front, blue points are on the Pareto Front
3D Scatter Plot of Pareto Front, blue points are on the Pareto Front

Pareto in 2d

Projections of pareto front into 2D, blue points are on the pareto front
Projections of pareto front into 2D, blue points are on the pareto front

Mixture Plots

Additive and Multiplicative Mixture Plots
Additive and Multiplicative Mixture Plots

More on Mixtures

  • Mixture plots don’t give a great picture. The tables below show the top five observations in overall percentage of plots above
5 best addative scores
9233 422 432 431 430
0.18 0.14 0.12 0.091 0.061
5 best multiplicative scores
9233 9229 432 310 392
0.17 0.076 0.045 0.03 0.03

Contour for Point 9233

Point Desireablity
Point Desireablity

Contour for Point 422

Point Desireablity
Point Desireablity

Contour for Point 432

Point Desireablity
Point Desireablity

Values of Selected Points

Table values for Point 9233
  Steep_Time Germ_Temp Kiln_Temp AM SOD DSD
9233 0.3 0.9 1 0.66 0.32 0.95
Table values for Point 432
  Steep_Time Germ_Temp Kiln_Temp AM SOD DSD
432 0.1 1 -1 0.14 0.88 1

Conclusions

Confirmation

AM SOD DSD
Rep1 1055.32 971.74 60.6
Rep2 1033.41 959.68 63.37
Rep3 1000.57 984.23 64.07
Rep4 1055.52 936.23 58.51
Model 1043.976 983.3642 6.06584
avg 1036.205 962.97 3.3625
Sdev.s 25.92372 20.45118 2.567507
Tstat 0.299749 0.997211 1.052905

L2

  • Large number of factors works against simplicity of design
    • Strong methodology can overcome (TWI vs. FO)
    • More variables = More noise
  • Progressive approach to analysis
    • First Order model then Second Order model
    • Discussion of Tradeoffs

Questions

Questions